Thornton has recorded 19 points in his last 24 games, including the last three. He has 48 points in 41 games against the Canucks.

The Sharks' fourth line got things going against Vancouver goalie Cory Schneider midway through the second period.

Desjardins scored his first goal of the season, and recorded his first point in 19 games, sneaking one past Schneider's glove side after taking a pass from Adam Burish, who netted his first point in 11 games.

Thornton scored his sixth goal of the season 41 seconds later, getting a pass from Matt Tennyson, who got credit for an assist on his NHL debut.

Thornton tried to pass the puck to Brent Burns but Christopher Tanev got his stick on it, deflecting it back to Thornton, who went top shelf on the right side.

Couture scored 92 seconds later, giving San Jose a 3-0 advantage. Thornton recorded one of the assists and now has 781 for his career, moving him into a tie for 34th, with Ryan Leach, on the all-time list.

Higgins got one of the goals back late in the period, getting a clear shot to Niemi's stick side after taking a pass from Jannik Hansen.

Higgins has scored twice in his last three games following an eight-game goal-less streak.

Schneider seemed up to the task of slowing down a potent Sharks attack through the first 27 minutes. After allowing two goals in the first three shots he faced in a loss to the Edmonton Oilers, he stopped the first 20 shots he faced Monday.

There was a particular sequence in the first period where he was under siege, deflecting a handful of close-up shots before finally covering the puck.

The Canucks also successfully killed off the first power play of the contest, but couldn't stop the league's top home team on the power play the next time around.

Earlier in the day, the Sharks acquired a fourth-round pick in the 2013 NHL Draft from the Chicago Blackhawks in exchange for veteran center Michal Handzus.

The Sharks and Blackhawks do not meet again during the regular season.

NOTES: Tennyson, who moved to the Bay Area when he was 15, became the first Sharks' player to participate in the Junior Sharks program as a youth. Tennyson was recalled from Worcester to replace the injured Jason Demers. ... Sharks left winger Ryane Clowe, the subject of trade rumors over the weekend, was a scratch, along with Demers. ... The Canucks recalled forwards Nicklas Jensen and Bill Sweatt from Chicago on Sunday in an attempt to invigorate their offense. Zach Kassic and Andrew Groton were reassigned. ... Mason Raymond and Andrew Alberts were scratches for the Canucks.